TSTP Solution File: ITP243^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP243^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 00:30:00 EDT 2022
% Result : Theorem 51.83s 51.78s
% Output : Proof 51.83s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_option_nat,type,
option_nat: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_vEBT_vebt_succ,type,
vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_vEBT_VEBT_set_vebt,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(ty_vEBT_is_succ_in_set,type,
vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_deg,type,
deg: nat ).
thf(ty_xa,type,
xa: nat ).
thf(ty_one,type,
one: num ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_sc,type,
sc: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
( ( ( vEBT_vebt_succ @ summary @ X1 )
= ( some_nat @ X2 ) )
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= ( some_nat @ X1 ) )
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= ( some_nat @ sc ) )
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) )
=> ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= ( some_nat @ sc ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o] :
( ( X1 @ ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) )
=> ! [X2: $o] :
( ( X2
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $o] :
( ( X1
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= ( some_nat @ sc ) )
= ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= ( some_nat @ sc ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP7
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP10
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
sP6,
inference(eq_ind_sym,[status(thm)],]) ).
thf(fact_1__092_060open_062vebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_092_060close_062,axiom,
sP9 ).
thf(fact_0__C4_Ohyps_C_I3_J,axiom,
sP1 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,fact_1__092_060open_062vebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_092_060close_062,fact_0__C4_Ohyps_C_I3_J,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP243^1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 10:50:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 51.83/51.78 % SZS status Theorem
% 51.83/51.78 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 51.83/51.78 % Inferences: 33
% 51.83/51.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------